I completely second a Omark 44 in 308, I think they are a truly underrated rifle... Allot of guy will tell you , you need a freakn RPA, Barnard etc to shoot fullbore and blow $3K just on a action.. Well, I've put mates onto $400 Omarks and they have shot plenty well out to 1km with the old iron sights..
If you really want to have a go at silly ranges, You can pop out to my property at Cecil Plains, I have a 1.2 km, 1.6 km and a 3.2 km range being built now. Or if you're feeling in a light hearted mood, You can shoot a Sharps out to 3.2 km... You know, Fire, we go make a cup of tea have some biscuits, and come back to look through the spotting scope with just enough time to see it hit a gong..